Design of a composite membrane with patches

Fabrizio Cuccu, Behrouz Emamizadeh, Giovanni Porru

Research output: Journal PublicationArticlepeer-review

6 Citations (Scopus)


This paper is concerned with minimization and maximization problems of eigenvalues. The principal eigenvalue of a differential operator is minimized or maximized over a set which is formed by intersecting a rearrangement class with an affine subspace of finite co-dimension. A solution represents an optimal design of a 2-dimensional composite membrane Ω, fixed at the boundary, built out of two different materials, where certain prescribed regions (patches) in Ω are occupied by both materials. We prove existence results, and present some features of optimal solutions. The special case of one patch is treated in detail.

Original languageEnglish
Pages (from-to)169-184
Number of pages16
JournalApplied Mathematics and Optimization
Issue number2
Publication statusPublished - Oct 2010
Externally publishedYes


  • Minimization and maximization problems
  • Optimal solutions
  • Principal eigenvalue
  • Rearrangements

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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